
Re: Matheology S 224
Posted:
Apr 14, 2013 11:29 PM


Nam Nguyen <namducnguyen@shaw.ca> writes:
> On 14/04/2013 7:40 PM, Jesse F. Hughes wrote: >> Nam Nguyen <namducnguyen@shaw.ca> writes: >> >>> On 14/04/2013 4:58 PM, Nam Nguyen wrote: >>>> On 14/04/2013 4:28 PM, Nam Nguyen wrote: >>>>> On 14/04/2013 3:41 PM, fom wrote: >>>>>> On 4/14/2013 3:40 PM, Nam Nguyen wrote: >>>>>>> On 14/04/2013 9:19 AM, Nam Nguyen wrote: >>>>>>>> On 14/04/2013 12:44 AM, Nam Nguyen wrote: >>>>>>>>> >>>>>>>>> Can you or they give me a straightforward statement of understanding >>>>>>>>> or not understanding of Def1, Def2, F, F' I've requested? >>> >>>> Also, if you'd like to help the debate about my cGC thesis, >>>> why don't you offer a closure on my Def1 and Def2. >>>> >>>> I'm serious in saying that it's crucial to my thesis about >>>> cGC. If such a simple definition of setmembership truthrelativity >>>> is technically wrong, inconsistent, or what have you, of course my >>>> entire thesis would falter to pieces. And you will never hear me attempt >>>> on the relativity of cGC truth anymore. >>>> >>>> But I do need a closure on these 2 definitions. >>> >>> Naturally _everyone_ who could constructively contribute to the closure >>> would be welcomed. And if I miss anyone in the below list I'd like >>> to apologize in advance. >>> >>> In particular, with some reasons no so important of my own, I'd >>> like appreciate in advance if Chris Menzel, Herman Rubin, Franz >>> Fritsche, Aatu Koskensilta, George Greene, Dave Seaman, Rupert, >>> Jim Burns, could offer some analysis and closure on my Def1 and Def2 >>> as presented in: >>> >>> http://groups.google.com/group/sci.math/msg/e6f47fad548fbb97?hl=en >> >> You sure seem eager for some comments. I know I'm not on the list, >> but I'll bite. > > First is my nontechnical caveat about the list of names. It obviously > can only be a finite list so any in which way I would have listed, > an apparent "offending" would occur however unintentionally. And I > did apologize in advance for that. To prove the point, after I sent > out the list I realized I forgot to mention Mike Oliver. The reason > for the finite list, as I've said is of _my own reason but isn't an_ > _important one_ . > > Based on some dialogs in the past, I believe correctly or incorrectly > those I mentioned _might_ be aware of some of the technical motivation > behind my presenting for years. That's all: just the motivation; I > certainly did _not_ chose the list based on who I'd think be "on my > side", so to speak. > > In any rate, I did invite "_everyone_ who could constructively > contribute ...". > >> >> , >>  Given a set S: >>  >>  Def1  If an individual (element) x is defined to be in S in a finite >>  manner or inductively, then x being in S is defined an absolute >>  truth. >>  >>  Def2  If an individual (element) x isn't defined to be in S in a >>  finite manner or inductively, then then x being in S, or not, >>  is defined as a relative truth, or falsehood, respectively >>  >>  Would you et al. understand Def1 and Def2 definitions now? >> ` >> >> I don't understand the definitions at all, because I don't know what >> it means that "x is defined to be in S in a finite manner or >> inductively." > > Let's do the finite case first, and I will address the "inductively" > case after. > > The finite case is the quite similar to the definition of FOL > syntactical theorems, where a proof of a formula is a _finite_ > _sequence of proofsteps_ conforming to a certain patterns (of > application of rules of inference). We have no choice but take > for granted what certain priori, "finite", "sequence", "steps", > etc... would mean. > > What Def1 says in the finite case is that given a set S, if an > element x is proven, verified to be in a nonempty _finite subset_ > of S then x being a member of S is defined to be an absolute truth. > Naturally here we also take for granted what it'd mean by "finite > subset", an element being in a set or not, to know or to verify an > element to be or not to be in a finite set, etc...
It seems to me that we are mixing syntactic and semantic notions here.
Do you mean: let t and s be any terms of the language of ZF (or whatever) and suppose that
ZF  (E x)(x c s & x != {} & x is finite & t in x)
then "t in s" is an absolute truth.
>> In fact, I understand almost none of that phrase. I don't know what >> it means for x to be "defined to be in S", much less so defined "in a >> finite manner or inductively". > > I'm not sure I understand your objection here: isn't defining a set S > is defining certain elements x's _to be in S_ ?
That's certainly not how I would put it. Is there any difference between the following two statements?
x is defined to be in S.
x is in S.
>> So, there you have it  a response > > Sure. Likewise I think I've explained your concern, in the finite case. > > Are you with me so far?
Not particularly, but we'll see how it goes.
 Jesse F. Hughes "It is not as satisfying to disagree with a book."  Russell Easterly, on why he argues against set theory without reading a book on set theory.

